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If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px + 4qy is?
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If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px...
Understanding the Ratios
Given the ratios:
- \( p : q = 2 : 3 \)
This means \( p = 2k \) and \( q = 3k \) for some constant \( k \).
- \( x : y = 4 : 5 \)
This implies \( x = 4m \) and \( y = 5m \) for some constant \( m \).
Substituting Values into the Expression
We need to evaluate the expression:
\[
\frac{5px + 3qy}{10px + 4qy}
\]
Substituting the values of \( p \), \( q \), \( x \), and \( y \):
- \( 5px = 5(2k)(4m) = 40km \)
- \( 3qy = 3(3k)(5m) = 45km \)
- \( 10px = 10(2k)(4m) = 80km \)
- \( 4qy = 4(3k)(5m) = 60km \)
Rewriting the Expression
Now substituting these results back into the expression:
\[
\frac{40km + 45km}{80km + 60km} = \frac{85km}{140km}
\]
Simplifying the Ratio
The \( km \) terms cancel out:
\[
\frac{85}{140}
\]
To simplify, we can divide both the numerator and denominator by 5:
\[
\frac{17}{28}
\]
Final Result
Thus, the value of \( 5px + 3qy : 10px + 4qy \) is:
\[
\frac{17}{28}
\]
Given the ratios:
- \( p : q = 2 : 3 \)
This means \( p = 2k \) and \( q = 3k \) for some constant \( k \).
- \( x : y = 4 : 5 \)
This implies \( x = 4m \) and \( y = 5m \) for some constant \( m \).
Substituting Values into the Expression
We need to evaluate the expression:
\[
\frac{5px + 3qy}{10px + 4qy}
\]
Substituting the values of \( p \), \( q \), \( x \), and \( y \):
- \( 5px = 5(2k)(4m) = 40km \)
- \( 3qy = 3(3k)(5m) = 45km \)
- \( 10px = 10(2k)(4m) = 80km \)
- \( 4qy = 4(3k)(5m) = 60km \)
Rewriting the Expression
Now substituting these results back into the expression:
\[
\frac{40km + 45km}{80km + 60km} = \frac{85km}{140km}
\]
Simplifying the Ratio
The \( km \) terms cancel out:
\[
\frac{85}{140}
\]
To simplify, we can divide both the numerator and denominator by 5:
\[
\frac{17}{28}
\]
Final Result
Thus, the value of \( 5px + 3qy : 10px + 4qy \) is:
\[
\frac{17}{28}
\]
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If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px + 4qy is?
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If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px + 4qy is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px + 4qy is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px + 4qy is?.
If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px + 4qy is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px + 4qy is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px + 4qy is?.
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